Variance and Standard Deviation of a Discrete PDF

The standard deviation for a discrete pdf, $P(X)$ is denoted by the Greek letter, sigma ($\sigma$), where

$$\sigma = \sqrt{\sum [x^2P(x)] - \mu^2}$$

Since the standard deviation is the square root of the variance, the variance is denoted by $\sigma^2$, where

$$\sigma^2 = \sum [x^2P(x)] - \mu^2$$

So to find the variance and standard deviation of a discrete pdf, P(''x''), one should:

  1. Find the mean of the distribution
  2. Find the squares of the values the random variable can assume
  3. Multiply each one of these squares by the probability that the corresponding random variable value occurs and then add all of these products together
  4. Subtract from this sum the squared mean of the distribution. This is the variance.
  5. Take the square root of the variance. This is the standard deviation.